Geometry Questions

Which of the following is equal to one O O cos 30 sin 60 cos 45 sin 60 cos 30 sin 45 O cos 45 sin 55

Question 6 If sin x 0 8 then what is the value of cos 90 x 0 2 0 4 O 0 6 Points 1 O 0 8

Simplify sec 900 8 cot 90 0 O csc tan 0 O sec 0 cot 0 O cos 0 sin 0 O sin 0 cos 0

Find the missing angle from the given figure 25 O 55 65 O 85 O 45

5 For the functions f x x 1 and g x x 5 fog x A x 4 x 25 x 26 D x 10x B C 25 E x 10x 26

Suppose that 3x 2y t and x t cos 0 Find at ax t and at ax y

Graph the image of the figure using th 1 reflection across the x axis K W

Find the minimum height h above the surface of Earth so that a pilot at point A in the figure can see an object on the horizon at C 145 mi away Assume 4 00 x 10 mi as the radius of Earth OCCES The minimum height is about mi Do not round until the final answer Then round to the nearest hundredth as needed 145 mi

9 1 9 3 Simplify these expressions 1 sec B cot B cot B cos B 2 csc B tan B tan B sin B 3 3 sin 2 x 1 cot 2 x 4 5 cos 2 x 1 tan 2 x 5 4 cos B tan B sin B 6 6 sin B cot B cos B

Geometry problems often require proving triangles are congruent Match the reason with the best pictorial representation A B A B C D A B 8 E D Choose AAS SSS HL ASA SAS Choose Choose Choose

The quadrilaterals ABCD and JKLM are similar Find the length x of JK C X B D X 14 8 S M

The pentagons JKL MN and PQRST are similar Find the length x of PQ X M 1 L 0 3 N K 2 S 0 6 R 2 4 1 8 T Q 0 6 P

b 0 A miles a B Two radar stations 6 miles apart are tracking an approaching airplane The angle of elevation from stations A and B to the plane is 61 and 27 respectively Calculate the distance between the airpla and stations A and B respectively Give your answer in miles and to two decimal places miles

Define the following To cut into two equal sections A numbering system used when measuring angles How far apart two points are from each other The ratio of a circle s circumference to its diameter Choose Choose Choose Choose

Define the following A figure resembling a stretched circle Part of a line using two points and all of the points between them The location half way between two point A curved figure resembling a valley Part of a line with a starting point and all of the Choose Choose Choose Choose Choose

From the following picture match the pairs of angles to the correct description of the angle relationship 2 7 1 8 5 8 3 7 1 2 3 5 6 7 8 Choose Choose Corresponding Angles Consecutive or Same Side Interior Angles Alternate Exterior Angles Vertical Angles

Match the following A triangle in which 2 sides have the same length A triangle in which all of the angles have the same measure A triangle in which one angle has a measure of 90 degrees A triangle in which all sides have the same length A triangle in which the 3 sides have Choose Choose Choose Choose Choose

1 Find the area of the quadrilateral 24 LA 10 4 M 5 4 3 2 1 2 H 1 2 4 S 1 2 3 4 5

7 If ZA 48 ZB 72 ZC 60 and the measures of the arcs are as indicated in the following figure find the measures of EF GH and DI A 100 D I B ENF 110 60 G H C

The figure shows a 700 foot tower on the side of a hill that forms a 7 angle with the horizontal Find the length of each of the two guy wires that are anchored 80 feet uphill and downhill from the tower s base and extend to the top of the tower how Transcribed Text 700 feet 80 feet J AIKAIPANNE TAKELT C 80 feet

A tank contains 9 000 L of brine with 19 kg of dissolved salt Pure water enters the tank at a rate of 90 L min The solution is kept thoroughly mixed and drair From the tank at the same rate a How much salt is in the tank after t minutes kg y b How much salt is in the tank after 30 minutes Round your answer to one decimal place y kg

1 2 3 4 5 in 15 81 11 7 14 m 13 42 11 15 16 16 11 10 in 14 m 15 12 1 m 8 in 15 56 14 m 12 13

y 2 tan 3x 2 1 Drag the movable black point to shift the function the red points to set the vertical asymptotes and the blue point at the correct set of coordinates You may click on a point to verify its coordinates Note that only one period of the function is shown Shift the given graph using the general form in order to ensure you are graphing the correct period Provide your answer below TE 211 3 5 11 3 4 3 2 2 1 4 1 2 0 0 71 3 T 2 1 21 3 IT

6 7 8 9 7 7 m 1 5 yd 5 8 m 6 m 5 9 in 14 9 ft ft 5 m 7 ft 6m 4 yd 15 1 ft 5 8 m 4 in

Sure arc 1 are 2 4 Find the measure of arc 1 round to one decimal place degrees wing two questions arc 2 5 Find the measure of arc 2 round to one decimal place degrees

Use the diagram for the following two questions 4x 3 6 Find the measure the arc degrees arc 7 Find the measure of the angle angle degrees

2 Find arc x degrees 409

8 Find angle x round to one decimal place degrees

A gardener designed a circular surrounded by bushes that approximate and equilateral triangle He planted bushes at each vertex of the triangle and at 6ft intervals along its boundary Each side of the triangle is tangent to the circle which has a radius of 6 3 ft how many bushes did he use by A 6 36 60640 869 sn B 18 D 54

In Exercises 17 to 22 use proportions to solve each problem 17 A recipe calls for 4 eggs and 3 cups of milk To prepare for a larger number of guests a cook uses 14 eggs How many cups of milk are needed

x 1 12 a N 2 7 x 1 b x 1 3 5 x 2

3 a 15 24 b 2 ft 2 yd 1 yd 3 ft c 2 m 150 cm 1 m 100 cm d 2 m 1 lb

5 Sarah ran the 300 m hurdles in 47 7 seconds In meters per second find the rate at which Sarah ran Give the answer to the nearest tenth of a meter per second

36 If the ratio of the measure of the complement of an angle the measure of its supplement is 1 4 find the measure of t angle

14 a x 1 X X x 1 b x 2 X 2x x 2

In Exercises 5 to 14 find the value of x in each proportion 7 21 24 5 a X 4 9 12 b X

1 State if the following statement is true or false If the statement is false then correct it If we perform the row operation R 2R R and then R3 2R R and then R3 2R R3 on the matrix we obtain 0 1 0 20 1 1 2 3 423 4 5 2 3 2 1 2 Use matrices and elementary row operations to solve the following system of equations 2x 3z 8 3x 3y 6z 9 x y z 5 2

Write a two column proof to show that the two triangles are congruent Given AB DE D B E C is the midpoint of AE and DB Prove AACB AECD

Identify the type and number of local extrema 8 6 80 60 40 20 20 40 60 80 y 2 4 6 8 X

32 A point of symmetry of the function f where f x a 3 4 b 3 5 c 3 4 d 3 4 x 3 4 is

Solve ABC subject to the given conditions if possible Round the lengths of the sides and measures of the angles in degrees to 1 decimal place if necessary Round Intermediate steps to at least four decimal places b 833 c 21 4 109 45 O The triangle with these conditions does not exist The triangle with these conditions does exist af B 0 C 0

es 153846 assignments 12018853 Write an equation for the line containing the point 1 3 and parallel to the line y x 6 9 10 perpendicular to the line y x 6 Write an equation for the line containing the point 5 3 and 11 parallel to the line y 4

8 perpendicular to the line y 2x 3

Write an equation for the line containing the point 2 3 and parallel to the line y 2x 3

A bowl is shaped like a hemisphere with diameter 60 cm A heavy ball with diameter 32 cm is placed in the bowl and water is poured into the bowl to a depth of h centimeters Find the volume V of water in the bowl Consider two cases one in which the ball is not completely submerged and the other in which it is V V 3 cm the ball is not completely submerged cm the ball is completely submerged

Use the formula for the present value of an ordinary annuity or the amortization formula to solve the following problem PV 15 000 i 0 01 PMT 550 n n Round up to the nearest integer

ind the unknown angles in triangle ABC for the following triangle if it exists C 45 20 b 25 4 m c 361 m Select the correct choice below and if necessary fill in the answer boxes to complete your choice OA There is only one possible set of remaining angles The measurements for the remaining angles are A Do not round until the final answers Then round to the nearest whole number as needed OB There are two possible sets of remaining angles The measurements for when B is larger are A and B O not round until the final answers Then round to the nearest whole number as needed OC No such trange exists and B and B The measurements for when B is smaller are

Suppose functions f x and g x are defined as follows x 1 2 3 f x g x 3 2 1 4 2 1 4 3 4 5 5 That is f 1 3 g 1 2 f 2 1 g 2 1 and so on Evaluate each of the following expressions ff 1 fog 2 gof 3 gog 4 5

An engineer designs a satelite dish with a parabolic cross section The dish is 18 ft wide at the opening and the focus is placed 9 ft from the verlex a Position a coordinate system with the origin at the vertex and the x axis on the parabola s axis of symmetry and find an equation of the parabola b Find the depth of the satellite dish at the vertex a The equation for the parabola is Type an equation Simplify your answer 180 G The figure may not be drawn to sca

10 If G is the midpoint of FH FG 14x 25 and GH 73 2x find